Fabrication of nanoscale T-shaped reentrant structures and its hydrophobic analysis

The present work proposes a facile method for fabricating robust hydrophobic surfaces with T-shaped reentrant nanostructures based on nano-patterning approach. The prepared surface demonstrates regularly arrangement over a large area. The hydrophobic stability of the prepared surface was analyzed theoretically using the Gibbs free energy approach, followed by being investigated experimentally. Experimental results show that the T-shaped reentrant nanostructures can significantly improve the hydrophobic stability of the surface, which is in line with the theoretical predictions. The proposed preparation method for T-shaped reentrant nanostructures provides a cost-effective and convenient way to fabricate robust hydrophobic surfaces.

Theoretical analysis of the hydrophobic robustness.In our calculations, we assume various values for the temporary apparent contact angle (0° < θ app < 180°) at a specified distance (x/H) of the liquid-air interface from the surface of T-shaped cap (normalized with respect to the height of T-shaped reentrant nanostructures H).Then the areal Gibbs free energy density (G*) of the liquid drop is calculated for each θ app and x/H.In order to facilitate easier visualization of the variation in the areal Gibbs free energy density of the T-shaped reentrant nanostructured surface, an uneven scale distribution of x-axis (x/H) was adopted in Fig. 2, which is based on the height of T-shaped cap (h = 20 nm) and the height of T-shaped pillar (H-h = 580 nm).
In Fig. 2a,b, a metastable composite interface corresponding to a global minimum in free energy is observed at x ~ 0, while a fully-wetted interface corresponding to a local minimum in free energy is observed at x ~ 600 nm.The liquid droplets keep in a metastable state with relatively low energy from x ~ 0 to x ~ 20 nm.There is a potential barrier at x ~ 20 nm as shown in Fig. 2c, and the liquid droplets from x ~ 0 to x ~ 20 nm would break through the barrier after being subjected to external pressure and reach x ~ 600 nm, which is a fully-wetted interface corresponding to a local minimum in free energy.
In Fig. 2d,e, a fully-wetted interface corresponding to a global minimum in free energy is observed at x ~ 600 nm, while a metastable composite interface corresponding to a local minimum in free energy is observed at x ~ 0. The liquid droplets keep in a metastable state with relatively low energy from x ~ 0 to x ~ 20 nm.There is a potential barrier at x ~ 20 nm as shown in Fig. 2f, and the liquid droplets from x ~ 0 to x ~ 20 nm would break through the barrier after being subjected to external pressure and reach x ~ 600 nm, which is a fully-wetted interface corresponding to a global minimum in free energy.

Surface wettability of T-shaped reentrant nanostructures
To evaluate the wetting properties, we selected five probing liquids with different surface tensions: hexadecane, toluene, olive oil, ethylene glycol, and DI water (see Table 2).The initial examination was conducted on a flat silicon surface coated with PFOTS (as depicted in Fig. 3).The measured θ app decreased with increasing liquid surface tension.Our observations showed that the apparent contact angle (θ app ) decreased with a decrease in liquid surface tension while the transition from wetting to non-wetting (θ app ≈ 90°) occurred at a critical surface tension (γ C ) of approximately 48.2 mN/m.Furthermore, the contact angle hysteresis (θ CAH ) remained around 20°.As expected, liquids with lower surface tensions exhibited wetting behavior on the smooth PFOTS/Si surface.In contrast, the wetting properties of the T-shaped reentrant nanostructured PFOTS/Si surface were also examined, and the results demonstrated that the surface displayed high contact angles and low contact angle hysteresis (less than 10°) for droplets of varying surface tensions.The inset shows optical image of DI water (transparent), olive oil (light yellow) and ethylene glycol (red) droplets on the T-shaped reentrant nanostructured PFOTS/Si surface.Notably, the T-shaped reentrant nanostructured surface exhibited structural colors when exposed to light.
Under dynamic impact conditions, the enhanced stability in withstanding the wetting transition has also been noted on the T-shaped reentrant PFOTS/Si surface.A high-speed digital camera was utilized to capture

Conclusions
In summary, we proposed a facile method to fabricate robust hydrophobic surfaces with T-shaped reentrant nanostructures.The prepared T-shaped reentrant nanostructures with regularly arrangement in a large area were demonstrated and the hydrophobic stability of the prepared surface was analyzed theoretically using the Gibbs free energy approach and experimentally.Experimental results show that the T-shaped reentrant nanostructures can significantly improve the hydrophobic stability of the surface, which is in line with the theoretical predictions.The proposed preparation method for T-shaped reentrant nanostructures provides a cost-effective and convenient way to fabricate robust hydrophobic surfaces.

Fabrication of T-shaped reentrant nanostructures
The through-hole anodic aluminium oxide (AAO) membranes were prepared by the well-known two-step anodization process (Fig. 5a) as our previous work 24 .The first anodization was carried out in 1% phosphoric acid and 0.01 M aluminum oxalate hydrate for 4 h at the temperature of 1 °C and voltage of 195 V. Perform a second anodization for 2.5 h under the same conditions.Subsequently, the pore-widening and pore-opening process was finished in 5% phosphoric acid solution for 50 min at 50 °C.The prepared AAO membranes were transferred onto the Si substrates in De-ionized (DI) water for keeping the membranes from twisting, folding and cracking (Fig. 5b).To achieve good mechanical robustness, a silicon wafer with the high Young's modulus  of Si (up to 66 GPa) is employed to obtain T-shaped reentrant nanostructure.Subsequently, an array of Cr nanoparticles with a thickness of approximately 50 nm was deposited onto the Si surface via AAO pores using electron beam evaporation (Fig. 5c).Then, the AAO membranes were removed with a commercial tape.The resulting Cr nanoparticle array on the Si substrates would serve as the subsequent etching template.The selective XeF 2 isotropic etching was employed to obtain T-shaped reentrant nanostructure on the Si substrate (Fig. 5d).
Finally, a T-shaped reentrant nanostructure was formed after removing Cr nanoparticles from the Si surface (Fig. 5e).Despite its reentrant structure, the surface must still undergo chemical modification for increased resistance to wetting, then samples were treated with 1H, 1H, 2H, 2H-perfluoro-octyltrichlorosilane (PFOTS, Sigma-Aldrich) in the vapor phase at 140 °C for 5 min 25 .

Theoretical modeling and simulation
A theoretical modeling of the wetting process, based on Marmur's 26 and Tuteja's works 25 , was used to calculate the change in the Gibbs free energy density with the evolution of the solid-liquid interface for evaluating the stability of a composite interface on the T-shaped reentrant surface.Based on geometric parameters in Fig. 6a and the coordinate system in Fig. 6b, the formulations of geometric parameters are built as shown in Table 3.
Based on the theoretical modeling, a Matlab® (Mathworks Inc.) code was developed, and the areal Gibbs free energy density (G*) variation of the liquid drop was computed for water (γ lv = 72.6 mN/m, θ = 120°) and hexadecane (γ lv = 27.5 mN/m, θ = 80°).Herein γ is the surface tension, and subscripts s, v, and l represent solid, vapor and liquid, respectively.
From the thermodynamic perspective, the areal Gibbs free energy density of a given volume of liquid droplet at equilibrium on a substrate is given by the following equation

Sample characterization
The fabricated Cr nanoparticles, unremoved AAO mask and T-shaped reentrant nanostructures were observed and their images were taken using field emission scanning electron microscopy (FESEM, FEI Nova NanoSEM 450).The liquid-repellent properties of liquid droplets on the sample surfaces were characterized using an optical contact-angle system (OCA20, Dataphysics, Germany).DI water of ∼ 5 μL and hexadecane (Sigma-Aldrich) drops of ∼ 2 μL were used as CA test solvents.To accurately express the wettability of the surface, the contact angle with 3-5 different positions on the surface was measured.
(1) Table 3. Formulations of geometric parameters for the hexagonal arrangement.Herein r f is the roughness of wetted solid, defined as the actual wetted surface area divided by its projected surface area, f s is the solid fraction, defined as the projected wetted surface area divided by the nominal surface area, θ int is the intrinsic contact angle on the smooth and flat surface, θ app is the apparent contact angle, G* is the areal Gibbs free energy density as a function of θ app and x/H.

Table 1 .Figure 2 .
Figure 2. The change in the areal Gibbs free energy density.(a) The variation in the areal Gibbs free energy density for water propagating on a hydrophobic (θ int = 120°) T-shaped reentrant nanostructured surface.(b) Top view of the energy diagram shown in (a).(c) Cross section view shown in (a).(d) The variation in the areal Gibbs free energy density for hexadecane propagating on an oleophilic (θ int = 80°) T-shaped reentrant nanostructured surface.(e) Top view of the energy diagram shown in (d).(f) Cross section view shown in (d).

Figure 3 .
Figure 3. Wetting properties of the different liquids on the flat and T-shaped reentrant PFOTS/Si surface.The inset is optical image of DI water (transparent), olive oil (light yellow) and ethylene glycol (red) droplets on the T-shaped reentrant nanostructured PFOTS/Si surface.

Figure 4 .
Figure 4.The surface of T-shaped reentrant nanostructured PFOTS/Si surface displayed the bouncing of hexadecane droplets as captured by a sequence of high-speed digital camera photograph.

Figure 5 .
Figure 5. Schematic diagram of the fabrication process for T-shaped reentrant nanostructures.(a) Two-step anodization, (b) through-hole AAO membrane fixed on a Si substrate as an evaporation mask, (c) depositing of the Cr nanoparticle array on the Si substrate, (d) selective XeF 2 isotropic etching of Si substrate using Cr nanoparticles as a mask, (e) removing Cr nanoparticles.

Figure 6 .
Figure 6.A schematic illustration of the topological profile in the calculation of the change in the Gibbs free energy density on the propagation of the liquid-air interface.(a) Geometric parameters in a discrete unit (blue area) with hexagonal arrangement, (b) the coordinate system used in the calculation.Herein D represents the diameter of T-shaped cap, d represents the diameter of T-shaped pillar, H represents the height of T-shaped reentrant nanostructures, h represents the height of T-shaped cap, P represents the pattern pitch of T-shaped reentrant nanostructures.

Table 2 .
The surface tension of tested liquids measured on the flat and T-shaped reentrant PFOTS/Si surface.